Some remarks on the mutually commutative idempotents

IF 0.8 Q2 MATHEMATICS Advances in Operator Theory Pub Date : 2024-06-03 DOI:10.1007/s43036-024-00339-4
Wei Luo, Chunhong Fu, Qingxiang Xu
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引用次数: 0

Abstract

This paper deals mainly with the idempotency of an operator or a matrix T given by \(T=c_1 \Pi _1 +c_2 \Pi _2+\cdots +c_n\Pi _n,\) where n is an arbitrary positive integer, \(\{\Pi _{1},\Pi _{2},\ldots ,\Pi _{n}\}\) is a collection of mutually commutative idempotents, and \(c_1,c_2,\ldots ,c_n\) are complex numbers. Some previous results in the cases of \(n=2\) and \(n=3\) are generalized, and meanwhile some new characterizations of the idempotency of T are obtained.

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本文主要讨论一个算子或矩阵 T 的幂等性,其公式为 \(T=c_1 \Pi _1 +c_2 \Pi _2+\cdots +c_n\Pi _n,\),其中 n 是任意正整数、\(\{Pi_{1},\Pi_{2},\ldots ,\Pi_{n}\})是相互交换的幂的集合,而(c_1,c_2,\ldots ,c_n\)是复数。对之前关于 \(n=2\) 和 \(n=3\) 的一些结果进行了归纳,同时得到了 T 的幂等性的一些新特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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CiteScore
1.60
自引率
0.00%
发文量
55
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